In Ruby, I need to draw from an exponential distribution with mean m. Please show me how to do it quickly and efficiently. Eg. let's have:
m = 4.2 def exponential_distribution rand( m * 2 ) end But of course, this code is wrong, and also, it only returns whole number results. I'm already tired today, please hint me towards a good solution.
If you want to do it from scratch you can use inversion.
def exponential(mean) -mean * Math.log(rand) if mean > 0 end If you want to parameterize it with rate lambda, the mean and rate are inverses of each other. Divide by -lambda rather than multiplying by -mean.
Technically it should be log(1.0 - rand), but since 1.0 - rand has a uniform distribution you can save one arithmetic operation by just using rand.
How about using the distribution gem? Here's an example:
require 'distribution' mean = 4.2 lambda = mean**-1 # generate a rng with exponential distribution rng = Distribution::Exponential.rng(lambda) # sample a value sample = rng.call If you need to change the value of lambda very often it might be useful to use the p_value method directly. A good sample can be found in the source code for Distribution::Exponential#rng, which basically just uses p_value internally. Here's an example of how to do it:
require 'distribution' # use the same rng for each call rng = Random 1.step(5, 0.1) do |mean| lambda = mean**-1 # sample a value sample = Distribution::Exponential.p_value(rng.rand, lambda) end 
m = λ^-1 you want to pass λ = m^-1 as argument (source: en.wikipedia.org/wiki/Exponential_distribution).